Geometric Interpretation of the Dot Product
5
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In this video I go over the geometric interpretation of the dot product and show that it can be written to include the angle between the 2 vectors. That is, a ⋅ b = |a| |b| cos θ. I also derive this formula using the law of cosines, which I first went over in my earlier video. I also go over several examples, as well as a corollary on determining the angle directly from 2 vectors.
The timestamps of key parts of the video are listed below:
- Geometric Interpretation: 0:00
- Definition 2: 3:17
- Example 2: 18:31
- Corollary: 21:17
- Example 3: 22:03
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: The Dot Product: https://youtu.be/9uqtIk5iHys
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GbHgvpTY1mx61nTNO-Msl8
Related Videos:
Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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